The authors report on comparative measurements of the optical properties of undoped AlAs/GaAs multiple quantum well (MQW) structures grown by conventional molecular beam epitaxy (MBE) and by migration-enhanced epitaxy (MEE). The structures were grown in pairs, one by MBE and one by MEE, at the same growth temperature which was varied between 530 degrees C and 680 degrees C. Growth conditions were monitored in all cases by observing RHEED oscillation behaviour and care taken to adjust the MEE conditions so that as nearly as possible each cycle of growth consisted of exactly one monolayer of the group III element. The growth structures were monitored by X-ray diffraction (XRD) and by low-temperature photoluminescence measurements. Analysis of the XRD results shows that the widths of the quantum wells are close to the expected value (75 AA) for the MBE samples for all growth temperatures but tend to be slightly high for the MEE samples. The AlAs/GaAs interfaces are broadened by about 2 monolayers for one interface and 3/4 monolayers for the other. For the MEE samples grown at 630 degrees C and 680 degrees C the XRD spectra show significant deterioration in quality, with large variations in QW period. Analysis of PL spectra shows good agreement of well widths with the XRD measurements but reveals an important difference between the MBE and MEE samples. The latter spectra are dominated by the presence of extrinsic luminescence whereas the former show only intrinsic exciton lines. The exciton linewidths are close to 3 meV for all the MBE samples but are about a factor two larger for MEE samples grown at 530 degrees C and 580 degrees C (the exciton transitions being completely swamped by extrinsic emission for higher growth temperatures). The luminescent efficiencies of the exciton lines in the MEE samples are about an order of magnitude lower than those in the MBE samples. Comparison of excitation and emission spectra from the MBE samples shows no measurable Stokes shift and, taken with the almost constant linewidths, suggests that the interfaces in these samples are all in the pseudo-smooth regime where the terrace lengths are smaller than the exciton diameter.